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High-field magnetization study of the S = 1/2 antiferromagnetic Heisenberg chain [PM Cu(NO$_3$)$_2$(H$_2$O)$_2$]$_n$ with a field-induced gap

We present a high-field magnetization study of the $S$ = 1/2 antiferromagnetic Heisenberg chain [PM Cu(NO$_3$)$_2$(H$_2$O)$_2$]$_n$. For this material, as result of the Dzyaloshinskii-Moriya interaction and a staggered $g$ tensor, the ground state is characterized by an anisotropic field-induced spin excitation gap and a staggered magnetization. Our data reveal the qualitatively different behavior in the directions of maximum and zero spin excitation gap. The data are analyzed via exact diagonalization of a linear spin chain with up to 20 sites and on basis of the Bethe ansatz equations, respectively. For both directions we find very good agreement between experimental data and theoretical calculations. We extract the magnetic coupling strength $J/k_B$ along the chain direction to 36.3(5) K and determine the field dependence of the staggered magnetization component $m_s$.